WASHINGTON—Former FBI Director James Comey revealed in a series of private memos that President Donald Trump and his then-chief of staff had doubts within days of taking office about national security adviser Mike Flynn, who subsequently left the administration after misleading officials about his contacts with Russia and later pleaded guilty to lying to law enforcement.

Mr. Comey’s previously unreported account of their take on Mr. Flynn was part of seven memos spanning 15 pages that were authored by Mr. Comey over a four-month period in 2017 and shared with Federal Bureau of Investigation leadership.

The memos were reviewed by The Wall Street Journal on Thursday after being handed over to several congressional committees by the Justice Department.

Much of the material in the memos has been previously disclosed. Mr. Comey has previously said he documented several encounters with the president in contemporaneous written memos. He also testified in Congress that he eventually provided several of them to reporters through an intermediary.

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Together, the memos provide Mr. Comey’s account of several meetings with the new president and his staff at a time when the FBI director faced uncertainty over whether he would be retained in his job by Mr. Trump.

They also provide a look at how the new president and administration grappled with a series of surprises, such as the leak of transcripts of Mr. Trump’s phone calls with the leaders of Mexico and Australia and salacious claims made in an unverified dossier that Mr. Comey brought to the president’s attention.

The documents are also part of the wide-ranging probe being conducted by special counsel Robert Mueller into Russian interference in the 2016 election, as well into whether Mr. Trump obstructed justice when he fired Mr. Comey last year, which Mr. Trump denies. Russia has denied interfering in the election.

Mr. Trump late Thursday tweeted, “James Comey Memos just out and show clearly that there was NO COLLUSION and NO OBSTRUCTION. Also, he leaked classified information. WOW! Will the Witch Hunt continue?’

The memos reveal that Mr. Trump expressed concerns about Mr. Flynn’s judgment just eight days after becoming president. Mr. Comey recounts a Jan. 2017 dinner with the president during which Mr. Trump said about Mr. Flynn: “The guy has serious judgment issues.” At issue was the fact that Mr. Flynn hadn’t told the president about a phone call from an unspecified foreign leader.

People familiar with the matter say that the call was from Russian President Vladimir Putin, who was the first foreign leader to call the White House to congratulate Mr. Trump after his inauguration. The call wasn’t brought to Mr. Trump’s attention until he was in the middle of a lunch with British Prime Minister Theresa May and was thanking her for being the first to call him.

Mr. Flynn piped up and explained that it was Mr. Putin, not Ms. May, who the first to call and that Mr. Trump was expected to return Mr. Putin’s call soon, the people said. According to the memo, Mr. Trump was furious “because six days was not an appropriate period of time to return a call.”

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Another memo documents Mr. Comey’s meeting with then-White House chief of staff Reince Priebus on Feb. 8, 2017. In that meeting, Mr. Priebus asked if Mr. Flynn was being surveilled under the Foreign Intelligence Surveillance Act. Surveillance under that law is reserved for suspected agents of a foreign government. Mr. Comey’s answer is redacted.

An attorney for Mr. Flynn declined to comment. Mr. Priebus didn’t immediately respond to a request for comment.

Mr. Comey testified for several hours last year in front of the Senate Intelligence Committee shortly after he was fired, telling lawmakers that he believed he was receiving an order when Mr. Trump said he “hoped” he would be able to end the FBI’s inquiry into Mr. Flynn.

“It’s my judgment that I was fired because of the Russia investigation,” Mr. Comey said.

Mr. Flynn pleaded guilty in December to lying about calls he had with Moscow’s ambassador a month before Mr. Trump’s inauguration. In a court hearing, Mr. Flynn admitted he misled FBI agents about a series of calls he had last December with the ambassador, Sergey Kislyak, in which they discussed sanctions imposed on Russia by the Obama administration and a United Nations resolution critical of Israel.

Mr. Flynn resigned in February 2017, acknowledging that he hadn’t been truthful about his contacts with Mr. Kislyak.

The memos also give Mr. Comey’s account of what he saw as Mr. Trump’s fixation on salacious and unverified rumors that he had engaged prostitutes in a Moscow hotel in 2013. A dossier compiled by an ex-British spy alleges that Mr. Trump watched as Russian prostitutes urinated on a bed where former President Barack Obama and his wife had slept.

Mr. Comey’s memos recall a February encounter in which Mr. Trump “brought up the ‘Golden Showers thing’ and said it really bothered him if his wife had any doubt about it.” Mr. Comey added: “The president said ‘the hookers thing’ is nonsense,” but also that Mr. Putin had told him that Russia had “some of the most beautiful hookers in the world.”

Capitol Hill Republicans—who had been pushing for the memos to be released publicly—said that the memos vindicated Mr. Trump, who has long argued that there was no collusion with Russia and that he didn’t obstruct justice in firing his FBI director.

“Former Director Comey’s memos show the president made clear he wanted allegations of collusion, coordination, and conspiracy between his campaign and Russia fully investigated,” Reps. Trey Gowdy, Bob Goodlatte and Devin Nunes said in a joint statement. The three Republicans chair the House Oversight, Judiciary and Intelligence committees, respectively.

Four of the memos were deemed to have classified information, while three are unclassified. Mr. Comey testified to Congress that they were his “unclassified memorialization” of conversations with the president. They were released to Congress with the classified information redacted. Unredacted versions will be available to members of Congress in a secure facility, according to the Justice Department.

Mr. Comey himself appeared to recognize that one of his memos contained information that was potentially classified. The memo, which was written in email form to three other FBI officials, contained a passage from Mr. Comey where he wrote: “I am not sure the proper classification here so I have chosen SECRET. Please let me know [if] it should be higher or lower than that.”

Mr. Comey is in the middle of a book tour for his memoir “A Higher Loyalty: Truth, Lies, and Leadership,” which is deeply critical of Mr. Trump.

In a series of tweets over the weekend, Mr. Trump accused Mr. Comey of telling lies in a “badly reviewed” book.